In WO98/57436 the concept of transposition was established as a method to recreate a high frequency band from a lower frequency band of an audio signal. A substantial saving in bitrate can be obtained by using this concept in audio coding. In an HFR based audio coding system, a low bandwidth signal is presented to a core waveform coder and the higher frequencies are regenerated using transposition and additional side information of very low bitrate describing the target spectral shape at the decoder side. For low bitrates, where the bandwidth of the core coded signal is narrow, it becomes increasingly important to recreate a high band with perceptually pleasant characteristics. The harmonic transposition defined in WO98/57436 performs very well for complex musical material in a situation with low cross over frequency. The principle of a harmonic transposition is that a sinusoid with frequency w is mapped to a sinusoid with frequency Qφω where Qφ>1 is an integer defining the order of the transposition. In contrast to this, a single sideband modulation (SSB) based HFR maps a sinusoid with frequency ω to a sinusoid with frequency ω+Δω where Δω is a fixed frequency shift. Given a core signal with low bandwidth, a dissonant ringing artifact will result from the SSB transposition.
In order to reach the best possible audio quality, state of the art high quality harmonic HFR methods employ complex modulated filter banks with very fine frequency resolution and a high degree of oversampling to reach the required audio quality. The fine resolution is necessary to avoid unwanted intermodulation distortion arising from the nonlinear treatment of sums of sinusoids. With sufficiently narrow subbands, the high quality methods aim at having at most one sinusoid in each subband. A high degree of oversampling in time is necessary to avoid alias type distortion, and a certain degree of oversampling in frequency is necessary to avoid pre-echoes for transient signals. The obvious drawback is that the computational complexity becomes very high.
Another common drawback associated with harmonic transposers becomes apparent for signals with a prominent periodic structure. Such signals are superimpositions of harmonically related sinusoids with frequencies Ω,2Ω,3Ω, . . . , where n is the fundamental frequency. Upon harmonic transposition of order Ωφ, the output sinusoids have frequencies QφΩ, 2QφΩ, 3QφΩ, . . . , which, in case of Qφ>1, is only a strict subset of the desired full harmonic series. In terms of resulting audio quality a “ghost” pitch corresponding to the transposed fundamental frequency QφΩ will typically be perceived. Often the harmonic transposition results in a “metallic” sounding character of the encoded and decoded audio signal.
In WO2010/081892, which is incorporated herein by reference, the method of cross products was developed to address the above ghost pitch problem in the case of high quality transposition. Given partial or transmitted full information on the fundamental frequency value of the dominating harmonic part of the signal to be transposed with higher fidelity, the nonlinear subband modifications are supplemented with nonlinear combinations of at least two different analysis subbands, where the distances between the analysis subband indices are related to the fundamental frequency. The result is to regenerate the missing partials in the transposed output, which however happens at a considerable computational cost.